spatstat (version 1.45-2)

rMaternII: Simulate Matern Model II

Description

Generate a random point pattern, a simulated realisation of the latex{Mat'ern}{Matern} Model II inhibition process.

Usage

rMaternII(kappa, r, win = owin(c(0,1),c(0,1)), stationary=TRUE, ...,
           nsim=1, drop=TRUE)

Arguments

kappa
Intensity of the Poisson process of proposal points. A single positive number.
r
Inhibition distance.
win
Window in which to simulate the pattern. An object of class "owin" or something acceptable to as.owin. Alternatively a higher-dimensional box of class "box3" or
stationary
Logical. Whether to start with a stationary process of proposal points (stationary=TRUE) or to generate the proposal points only inside the window (stationary=FALSE).
...
Ignored.
nsim
Number of simulated realisations to be generated.
drop
Logical. If nsim=1 and drop=TRUE (the default), the result will be a point pattern, rather than a list containing a point pattern.

Value

  • A point pattern if nsim=1, or a list of point patterns if nsim > 1. Each point pattern is normally an object of class "ppp", but may be of class "pp3" or "ppx" depending on the window.

Details

This algorithm generates one or more realisations of latex{Mat'ern}{Matern}'s Model II inhibition process inside the window win.

The process is constructed by first generating a uniform Poisson point process of ``proposal'' points with intensity kappa. If stationary = TRUE (the default), the proposal points are generated in a window larger than win that effectively means the proposals are stationary. If stationary=FALSE then the proposal points are only generated inside the window win. Then each proposal point is marked by an ``arrival time'', a number uniformly distributed in $[0,1]$ independently of other variables. A proposal point is deleted if it lies within r units' distance of another proposal point that has an earlier arrival time. Otherwise it is retained. The retained points constitute latex{Mat'ern}{Matern}'s Model II.

The difference between latex{Mat'ern}{Matern}'s Model I and II is the italicised statement above. Model II has a higher intensity for the same parameter values.

See Also

rpoispp, rMatClust, rMaternI

Examples

Run this code
X <- rMaternII(20, 0.05)
 Y <- rMaternII(20, 0.05, stationary=FALSE)

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